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Capillary breakup of a liquid torus

Published online by Cambridge University Press:  01 February 2013

Hadi Mehrabian  and
James J. Feng
Hadi Mehrabian
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
James J. Feng*
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
†Email address for correspondence: jfeng@math.ubc.ca
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Abstract

Capillary instability of a Newtonian liquid torus suspended in an immiscible Newtonian medium is computed using a Cahn–Hilliard diffuse-interface model. The main differences between the torus and a straight thread are the presence of an axial curvature and an external flow field caused by the retraction of the torus. We show that the capillary wave initially grows linearly as on a straight thread. The axial curvature decreases the growth rate of the capillary waves while the external flow enhances it. Breakup depends on the competition of two time scales: one for torus retraction and the other for neck pinch-off. The outcome is determined by the initial amplitude of the disturbance, the thickness of the torus relative to its circumference, and the torus-to-medium viscosity ratio. The linearly dominant mode may not persist till nonlinear growth and breakup. The numerical results are generally consistent with experimental observations.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , pp. 281 - 292
Copyright
©2013 Cambridge University Press

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